Human cancers are sustained in their growth by a pathological counterpart of normal adult stem cells, cancer stem cells. This concept was first described in human myeloid leukemias and has later been extended to solid tumors such as breast and brain cancer. A quantitative understanding of cancer stem cells requires a mathematical framework to describe the dynamics of cancer initiation and progression, the response to treatment, and the evolution of resistance. In this proposal, we suggest to use mathematical and experimental techniques to investigate the biology of cancer stem cells. We will derive mathematical models to investigate the cell of origin of human cancers, the behavior of cancer stem cells during therapy, and the evolution of resistance to anti-cancer drugs. We will use chronic myeloid leukemia (CML) treated with ABL tyrosine kinase inhibitors as a particular example and will validate the predictions of the mathematical models in a murine model of CML. Our approach will provide a validated quantitative understanding of cancer stem cells, and allow us to apply mathematical modeling of cancer stem cells to biologically and clinically important issues including response to targeted therapies and evolution of drug resistance. The Specific Aims are 1. To design a mathematical framework of CML stem cells. 2. To validate the predictions derived in Aim 1 in a murine model of CML. 3. To study the dynamics of resistance to anti-cancer therapy. 4. To investigate the cell of origin of CML. The research program outlined in this proposal will establish a quantitative understanding of tumor stem cells in cancer initiation, progression, treatment, and resistance and will provide theoretical frameworks indispensable for the understanding of cancer stem cell biology and the optimum administration of therapies. We will also test our mathematical models in an in vivo system, in order to demonstrate the relevance of our mathematical models to an experimental model. Although outside the scope of this proposal, the ultimate goal of this research program is to use mathematical models to develop a general framework for evaluating the role of cancer stem cells in oncogenesis, and to develop specific therapies which target cancer stem cells for human malignancies.